Panconnectivity and Pancyclicity of Hypercube-Like Interconnection Networks with Faulty Elements

  • Jung-Heum Park
  • Hyeong-Seok Lim
  • Hee-Chul Kim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4331)


In this paper, we deal with the graph G 0G 1 obtained from merging two graphs G 0 and G 1 with n vertices each by n pairwise nonadjacent edges joining vertices in G 0 and vertices in G 1. The main problems studied are how fault-panconnectivity and fault-pancyclicity of G 0 and G 1 are translated into fault-panconnectivity and fault-pancyclicity of G 0G 1, respectively. Applying our results to a subclass of hypercube-like interconnection networks called restricted HL-graphs, we show that in a restricted HL-graph G of degree m (≥3), each pair of vertices are joined by a path in G \F of every length from 2m–3 to |V(G \F)| − 1 for any set F of faulty elements (vertices and/or edges) with |F| ≤m–3, and there exists a cycle of every length from 4 to |V(G \F)| for any fault set F with |F| ≤m–2.


Interconnection Network Hamiltonian Cycle Free Edge Longe Path Hamiltonian Path 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jung-Heum Park
    • 1
  • Hyeong-Seok Lim
    • 2
  • Hee-Chul Kim
    • 3
  1. 1.School of Computer Science and Information EngineeringThe Catholic University of KoreaKorea
  2. 2.School of Electronics and Computer EngineeringChonnam National UniversityKorea
  3. 3.Computer Science and Information Communications Engineering DivisionHankuk University of Foreign StudiesKorea

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